Arizona and Florida Have Primaries Today. Here’s What to Watch.

Republicans are facing off for a shot at replacing an anti-Trump senator in Arizona, while Democrats clash to get on the ticket in the Florida governor’s race.

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Representative Martha McSally is one of three candidates in Arizona’s Republican primary for Senate.CreditCreditMatt York/Associated Press

The primaries in Arizona and Florida on Tuesday will largely conclude a Republican nominating season dominated by President Trump, while also offering revealing insights into the direction of a Democratic Party wrestling with the way forward.

The Times will have live results starting at 7 p.m., when polls close in Florida.

Here are the most interesting races to watch:

Race to replace a Trump critic

The most high-profile race of the day may be the Republican Senate primary in Arizona, which illustrates how central Mr. Trump has become in Republican politics (and comes only three days after Arizona’s senior senator, John McCain, died of brain cancer). The race to replace Senator Jeff Flake, a Republican and an outspoken Trump critic who is retiring after a single term, has become a competition to see who can cling most tightly to Mr. Trump and his brand of hard-line conservatism.

The best-known figure in the three-way contest is Joe Arpaio, the former Maricopa County sheriff whom Mr. Trump pardoned last year, though he has been trailing in the polls. Mr. Arpaio’s presence in the race, however, has made it difficult on another hard-liner, Kelli Ward, to consolidate support from the most conservative Arizona voters.

With Mr. Arpaio siphoning votes, Ms. Ward, a former state senator who won nearly 40 percent against Mr. McCain in 2016, has gone to great lengths to garner attention on the right, inviting controversial conservatives to campaign with her and even suggesting Mr. McCain’s family tried to undercut her by putting out word last week that he was ending treatment for his cancer.

Representative Martha McSally, the establishment favorite in the race, has benefited from the divide on the right and could win without capturing a majority of the vote. But to prove her bona fides to Arizona’s conservative primary voters, and to keep the president from wading into the race against her, Ms. McSally has embraced Mr. Trump in ways that could create difficulties for her in the general election. Democrats are poised to nominate Representative Kyrsten Sinema, who has run a cautious campaign and has carefully avoided criticizing Mr. Trump, in an attempt at winning over the state’s center-right electorate.

Testing Arizona’s appetite for the left

In the Arizona governor’s race, Gov. Doug Ducey, a Republican, is expected to easily win renomination but could face a stiff challenge in November. And Democrats are deciding Tuesday between two candidates who are running very different campaigns.

David Garcia, a former executive at the state education department, has sought to rally progressives in Arizona and beyond by denouncing the Immigration and Customs Enforcement agency and asking activists to “imagine no wall in southern Arizona.”

Meanwhile, his opponent, State Senator Steve Farley, has run a far more moderate campaign, arguing that Democrats can only win in a red-tinted state by presenting themselves as pragmatists.

Florida’s Democrats could be a proving ground for the party

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Andrew Gillum, center, has been endorsed by Senator Bernie Sanders in the Democratic race for Florida governor.CreditJosh Ritchie for The New York Times

In Florida, Democrats are facing a similar dilemma about whether to follow their hearts or their heads in the governor’s race. Gwen Graham, a former congresswoman and the daughter of Bob Graham, is seen by many party officials as the candidate best positioned to appeal to the political middle in America’s largest swing state. And Philip Levine, the mayor of Miami Beach, has remained competitive thanks in part to spending nearly $30 million of his own money.

But Mayor Andrew Gillum of Tallahassee, who would be Florida’s first black governor, has positioned himself as the most liberal candidate in the race and has come on strong at the end of the primary. To win the general election, Mr. Gillum argues, Democrats need a candidate who can motivate young and nonwhite voters who often do not vote in midterm elections.

The Republican race to succeed the term-limited Gov. Rick Scott was upended in June when Mr. Trump endorsed Representative Ron DeSantis, propelling the 39-year-old congressman into a lead over Adam Putnam, the state agriculture commissioner and putative favorite. No Republican in the country may owe his primary success to Mr. Trump as much as Mr. DeSantis, should he win Tuesday. Mr. Putnam, a former state lawmaker and member of Congress, had been planning to run for governor for at least a decade. And he was widely seen as the favorite until Mr. Trump intervened in the race to reward Mr. DeSantis, who frequently appears on Fox News to defend the president.

Jonathan Martin is a national political correspondent. He has reported on a range of topics, including the 2016 presidential election and several state and congressional races, while also writing for Sports, Food and the Book Review. He is also a CNN political analyst. @jmartnyt